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Asian Power Electronics Journal, Vol. 7, No. 2, Dec. 2013

i

Asian Power

Electronics

Journal

PERC, HK PolyU

Asian Power Electronics Journal, Vol. 7, No.2, Dec. 2013

ii

Copyright © The Hong Kong Polytechnic University 2013. All right reserved.

No part of this publication may be reproduced or transmitted in any form or by any means, electronic or

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permission in writing form the publisher.

First edition Dec 2013 Printed in Hong Kong by Reprographic Unit

The Hong Kong Polytechnic University

Published by

Power Electronics Research Centre

The Hong Kong Polytechnic University

Hung Hom, Kowloon, Hong Kong

ISSN 1995-1051

Disclaimer

Any opinions, findings, conclusions or recommendations expressed in this material/event do not

reflect the views of The Hong Kong Polytechnic University

ii

Asian Power Electronics Journal, Vol. 7, No. 2, Dec. 2013

iii

Editorial board

Honorary Editor

Prof. Fred C. Lee Electrical and Computer Engineering, Virginia Polytechnic Institute and State University

Editor

Prof. Yim-Shu Lee

Victor Electronics Ltd.

Associate Editors and Advisors

Prof. Philip T. Krien

Department of Electrical and Computer Engineering, University of Illinois

Prof. Keyue Smedley

Department of Electrcial and Computer Engineering, University of California

Prof. Muhammad H. Rashid

Department of Electrical and Computer Engineering, University of West Florida

Prof. Dehong Xu

College of Electrical Engineering, Zhejiang University

Prof. Hirofumi Akagi

Department of Electrical Engineering, Tokyo Institute of Technology

Prof. Xiao-zhong Liao

Department of Automatic Control, Beijing Institute of Technology

Prof. Wu Jie

Electric Power College, South China University of Technology

Prof. Hao Chen

Dept. of Automation, China University of Mining and Technology

Prof. Danny Sutanto

Integral Energy Power Quality and Reliability Centre, University of Wollongong

Prof. S.L. Ho

Department of Electrical Engineering, The Hong Kong Polytechnic University

Prof. Eric K.W. Cheng


Dr. Norbert C. Cheung


Dr. Edward W.C. Lo


Dr. David K.W. Cheng

Department of Industrial and System Engineering, The Hong Kong Polytechnic University

Dr. Martin H.L. Chow

Department of Electronic and Information Engineering, The Hong Kong Polytechnic University

Dr. Frank H.F. Leung

Department of Electronic and Information Engineering, The Hong Kong Polytechnic University

Dr. Chi Kwan Lee

Department of Electrical and Electronic Engineering, The University of Hong Kong

Asian Power Electronics Journal, Vol. 7, No.2, Dec. 2013

iv

Publishing Director: Prof. Eric K.W. Cheng Department of Electrical Engineering, The Hong Kong Polytechnic University

Communications and Development Director: Ms. Anna Chang Department of Electrical Engineering, The Hong Kong Polytechnic University

Production Coordinator: Ms. Xiaolin Wang and Dr. James H.F. Ho Power Electronics Research Centre, The Hong Kong Polytechnic

University

Secretary: Ms. Kit Chan Department of Electrical Engineering, The Hong Kong Polytechnic University

S. K. Rai R. VarmaS. JangidP. Tandon

Asian Power Electronics Journal, Vol. 7, No. 2, Dec 2013

v

Table of Content

Improve the Performance of Intelligent PI Controller for Speed

Control of SEDM using MATLAB

A. K. Singh, A.K. Pandey and M. Mehrotra

45

Control Strategy with Game Theoretic Approach in DC Micro-grid

Mingxuan Wu, Lei Dong, Furong Xiao and Xiaozhong Liao

54

Three Phase Double Boost PFC Rectifier Fed SRM Drive

M. Rajesh and B. Singh

61

A Novel Seven-Level Inverter System for DTC Induction Motor Drive

O.C. Sekhar and K.C. Sekhar

68

Transformer-less Pulse Power Supply: A Prototype Development

, , and

Author Index

75

A. K. Singh et. al: Improve the Performance of Intelligent…

45

Improve the Performance of Intelligent PI Controller for

Speed Control of SEDM using MATLAB

A. K. Singh

1 A.K. Pandey

2 M. Mehrotra

3

Abstract–In this paper a new approach is develop for speed

control of separately excited D.C. motor by enhancing the

feature of artificial neural networks (ANN).The development

of artificial Neural Network controller for D.C. drives is

inspired by the ANN control strategy. The aim of the

proposed schemes is to improve dynamic performance of

separately excited D.C. motor [6]. The ANN concept is

applied for both control strategy i.e. current and speed for

D.C. separately excited motor. This new concept enhances the

performance and dynamics of D.C. motor in comparison to

conventional PI controllers and this is verified through

simulation using MATLAB/SIMULINK. Keywords–DC motor, ANN, PI controller, NARMA-L2

controller

I. INTRODUCTION

The separately excited Direct current (DC) motors with

conventional Proportional Integral (PI) speed controller

are generally used in industry. This can be easily

implemented and are found to be highly effective if the

load changes are small. However, in certain applications,

like rolling mill drives or machine tools, where the system

parameters vary substantially and conventional PI or PID

controller is not preferable due to the fact that, the drive

operates under a wide range of changing load

characteristics.

The artificial neural network (ANN), often called the

neural network, is the most generic form of Artificial

Intelligence for emulating the human thinking process

compared to the rule-based Expert system and Fuzzy

Logic [2]. Multilayer neural networks have been applied in

the identification and control of dynamic systems. The

three typical commonly used neural network controllers:

model predictive control, NARMA-L2 control, and model

reference control are representative of the variety of

common ways in which multilayer networks are used in

control systems. As with most neural controllers, they are

based on standard linear control architectures [3].There are

a number of articles that use ANNs applications to identify

the mathematical D.C. motor model and then this model is

applied to control the motor speed [4]. They also use

inverting forward ANN with input parameters for adaptive

control of D.C. motor [5].

This paper address the study of steady-state and dynamics

control of dc machines supplied from power converters

The paper first received 9 Jan 2013 and in revised form 28 July 2013.

Digital Ref: APEJ-2013-04-412 1 Department of Electrical Engineering, M. M. M. Engineering College,

Gorakhpur (U.P.), India, E-mail: er,[email protected] 2 Department of Electrical Engineering, M. M. M. Engineering College,

Gorakhpur (U.P.), India, E-mail: [email protected] 3

Department of Electrical Engineering, M. M. M. Engineering College,

Gorakhpur (U.P.), India, E-mail: [email protected]

and their integration to the load. This paper a comparative

study of artificial neural networks over conventional

controller such as PI speed and current controller. With the

help of transfer function models, analysis of the

performance of the dc motor drives for different cases has

been done.

II. TWO-QUADRANT THREE-PHASE CONVERTER

CONTROLLED DC MOTOR DRIVE

The control schematic of a two converter controlled

separately excited dc motor is shown in Fig.1. The

thyristor bridge converter gets its ac supply through a three

phase transformer and fast acting ac contactors. The field

is separately excited, and the field supply cannot be kept

constant or regulated. The DC motor has a tacho-generator

whose output is utilized for closing the speed loops. The

motor is driving a load considered to be frictional for this

treatment. The output of the tacho-generator is filtered to

remove the ripples to provide the signal, ωmr. The speed

command and ωr* is compared to the speed signal to

produce a speed error signal. This signal is processed

through a proportional plus integrator (PI) controlled to

determine the torque command. The torque command is

limited, to keep it within the safe current limits. The

armature current command ia* is compared to the actual

armature current ia to have a zero current error. In case,

there is an error, a PI current controller process it to alter

the control signal vc. The control signal accordingly

modifies the triggering angle α to be sent to the converter

for implementation [2]. The operation of closed speed

controlled drive is explained from one or two particular

instances of speed command. A speed from zero to rated

value is commanded, and the motor is assumed to be at

standstill, this will generate a large speed error and a

torque command and in turn an armature current command.

The armature current error will generate the triggering

angle to supply a preset maximum dc voltage across the

motor terminals.

cos1

cH

Three phase

a c s u p p l y

T r a n s f o r m e r

Fast act ing contactors

F i e l d

S p e e d

controller

C u r r e n t

controllerL i m i t e r B r i d g e

converter

Armature

Techogenerator

Load

F i l t e r

+-

+-

*

eT*

ai

ai

cV

*

r

m

mr

Fig.1: Speed –controlled two quadrant dc motor drive

mailto:[email protected]


46

The inner current loop will maintain the current at level

permitted by its commanded value. When the rotor attains

the commanded value, the torque command will settle

down to a value equal to the sum of load torque and other

motor losses to keep the motor in steady state. The design

of the gain and time constant of the speed and current

controllers is of paramount importance in meeting the

dynamic specifications of the motor drives.

III. MODELING AND DESIGN OF SUBSYSTEMS

A. DC motor and load

The dc machine contains an inner loop due to the induced

emf. It is not physically seen; it is magnetically coupled.

The inner current loop will cross this back-emf loop,

creating a complexity in the development of the model.

The development of such a block diagram for the dc

machine is shown in Fig.2. The load is assumed to be

proportional to speed and is given as

mll BT (1)

To decouple the inner current loop from the machine-

inherent induced-emf loop, it is necessary to split the

transfer function between the speed and voltage into two

cascade transfer functions, first between speed and

armature current and then between armature current and

input voltage, represented as

)(

)(

)(

)(

)(

)(

sV

sI

sI

s

sV

s

a

a

a

m

a

m

(2)

( ) (1 )

m b

a t m

s K

I s B sT

(3)

1

1 2

(1 )

( ) (1 )(1 )

a m

a

I s sTK

V s sT sT

(4)

m

t

JT

B

(5)

1t lB B B (6)

)(sGs )(sGc )(sGr )1)(1(1

21

1sTsT

sTK m

m

tb

sT

BK

1

cH

)(sG

*

r*

ai

mr

aVcVai mr

Speed

controllerLimiter

Current

controller

Converter

+-

+-

Fig.2: Block diagram of the motor drive

a

tab

a

at

a

at

JL

BRK

L

B

J

B

L

B

J

B

TT

22

21

4

1

2

11,

1

(7)

tab

t RRK

BK

21 (8)

B. Design of Controllers

The design of control loops starts from the innermost

(fastest) loop and proceeds to the slowest loop, which in

this case is the outer speed loop. The reason to proceed

from the inner to the outer loop in the design process is

that the gain and time constants of only one controller at a

time are solved. Instead of solving for the gain and time

constants of all the controllers simultaneously not only

that is logical; it also has a practical implication. Note that

every motor drive need not be speed controlled but may be

torque-controlled, such as for a traction application. In that

case, the current loop is essential and exists regardless of

whether the speed loop is going to be closed. Additionally,

the performance of the outer loop is dependent on the

inner loop; therefore, the tuning of the inner loop has to

precede the design and tuning of the outer loop.

a. Current Controller

The current control loop is shown in Fig.3. the loop gain

function is

)1)(1)(1(

)1)(1()(

21

1

r

mc

c

crci

sTsTsTs

sTsT

T

HKKKsGH

(9)

This is a fourth-order system, and simplification is

necessary to synthesize a controller without resorting to a

computer. Noting that Tm is on the order of a second and in

the vicinity of the gain crossover frequency, we see that

the following approximation is valid:

mm sTsT )1( (10)

this reduces the loop gain function to

)1)(1)(1(

)1()(

21 r

ci

sTsTsT

sTKsGH

(11)

where

c

mcrc

T

THKKKK 1 (12)

the time constants in the denominator are seen to have the

relationship

12 TTTr (13)

The equation (11) can be reduced to second order, to

facilitate a simple controller synthesis, by judiciously

selecting

2TTc (14)

Then the loop function is


47

)1)(1()(

1 ri

sTsT

KsGH

(15)

+-

*

ai cV aV ai

ami

cH

c

cc

sT

sTK )1(

r

r

sT

K

1 )1)(1(

1

21

1sTsT

sTK m

Fig. 3: Current control loop

The characteristic equation or denominator of the transfer

function between the armature current and its command is

KsTsT r )1)(1( 1 (16)

this equation is expressed in standard form as

rrr

TT

K

TT

TTssTT

11

2121

1 (17)

From which the neural frequency and damping ratio are

obtained as

r

nTT

K

1

2 1 (18)

r

r

r

TT

K

TT

TT

1

1

1

12

(19)

where n and are the natural frequency and damping

ratio, respectively. For good dynamic performance, it is an

accepted practice to have a damping of 0.707.Hence,

equating the damping ratio to 0.707 in equation (19), we

get

r

r

r

TT

TT

TT

K

1

2

1

1

21

(20)

Realizing that

1K (21)

rTT 1 (22)

Tells us that K is approximated as

rr T

T

TT

TK

22

1

1

21 (23)

by equating equation (12) to (23).the current-controller

gain is evaluated

mcrr

cc

THKKT

TTK

1

1 1

2

1 (24)

b. Speed Controller The speed loop with the first-order approximation of the

current-control loop is shown in Fig.4.The loop gain

function is

)1)(1)(1(

)1()(

1 sTsTsTs

sT

TB

HKKKsGH

m

s

st

wbiss

(25)

This is a fourth-order system. To reduce the order of the

system for analytical design of the speed controller,

approximation serves. In the vicinity of the gain crossover

frequency, the following is valid

mm sTsT )1( (26)

The next approximation is to build the equivalent time

delay of the speed feedback filter and current loop. Their

sum is very much less than the integrator time constant Ts

and hence the equivalent time delay, T4 can be considered

the sum of the two delays, Ti and T . This step is very

similar to the equivalent time delay introduced in the

simplification of the current loop transfer function.Hence,

the approximate gain function of the speed loop is

)1(

)1()(

422 sTs

sT

T

KKsGH s

s

ss

(27)

where

TTT i 4 (28)

mt

bi

TB

HKKK 2 (29)

s

ss

sT

sTK )1(

11 sT

K i

sT

H

1

m

tb

sT

BK

1

*

r m

mr

*

ai ai+

-

Fig.4: Representation of the outer speed loop in the dc motor

drive

The closed loop transfer function of speed to its command

is

)(

)(1

)1(1

)(

)(

33

2210

10

222

24

3

2

*

sasasaa

aa

H

T

KKKKsTs

sTT

KK

Hs

s

s

s

s

s

s

r

m

(30)

where

ss TKKa /20 (31)


48

sKKa 22 (32)

12 a (33)

43 Ta (34)

This transfer function is optimized to have a wider

bandwidth and a magnitude of one over a wide frequency

range by looking at its frequency response. Its magnitude

is given by

})2()2({

1

)(

)(

23

623

631

22

420

21

220

21

220

*

aaaaaaaaa

aa

H

j

j

r

m

(35)

This is optimized by making the coefficients and

equal to zero, to yield the following conditions

2021 2 aaa (36)

3122 2 aaa (37)

Substituting these conditions in terms of the motor and

controller parameters given in (31) into (34) yields

2

2 2

KK

TT

s

ss (38)

Resulting in

2

2

KKT ss (39)

Similarly

2

42

22

2

2 2

KK

TT

KK

sT

s

s

s

s (40)

Thus after simplification, gives the speed – controller gain

as

422

1

TKK s (41)

Substituting equation (41) into equation (39) gives the

time constant of the speed controller as

44TTs (42)

Substituting for Ks and Ts into equation (38) gives the

closed-loop transfer function of the speed to its command

as

334

224

2244

4

* 88841

411

)(

)(

sTsTsTsT

sT

Hs

s

m

m

(43)

It is easy to prove that for the open-loop gain function the

corner points are1/4T4 and 1/T4, with the gain crossover

frequency being 1/2T4.

IV. NARMA-L2 CONTROL

The central idea of this type of control is to transform

nonlinear system dynamics into linear dynamics by

canceling the nonlinearities. This section begins by

presenting the companion form system model and

demonstrating how you can use a neural network to

identify this model [11]. Then it describes how the

identified neural network model can be used to develop a

controller. The tapped delay line (TDL), to make full use

of the linear network. There the input signals enter from

the left and passes through N-1 delays. The output of the

tapped delay line (TDL) is an N-dimensional vector, made

up of the input signal at the current time, the previous

input signal. Using the NARMA-L2 model, you can obtain

the controller.

)1(,),(),1(,),()1(,),(),1(,),([)(

)1(

mkukunkykyg

nkukunkykyfdky

ku

r

(44)

which is realizable for d ≥ 2.

Fig.5: Block diagram of the NARMA-L2 controller

This controller can be implemented with the identified

NARMA-L2 plant model, as shown in the Fig.6.

Fig. 6: Identified NARMA-L2 plant model

V. SIMULINK MODEL AND RESULTS

A. Response of the system using current and speed control

strategy with conventional PI controller


49

Fig.7: Simulink plant model with speed and current controller

In this control strategy, current control and speed control

are applying for improving the performance of DC motor

drive. In Fig.7.Shows the simulation plant model for this

case. The responses are shown in Fig.8(a) and 8(b).

B. Control strategy with ANN controller (NARMA-L2

CONTROL)

In this text consider the simulink modeling of a separately

excited DC motor with speed and current controller using

ANN. The entire conventional PI controller is replaced by

ANN. The control system of DC motor using neural

networks is presented. In this case study where use the

either single neural network as a controller for the control

the speed of DC drive with using Both control strategy.

The performance of DC motor drive with ANN controller

is evaluated by simulink plant model. The plant input and

output data are generated by neural network tools of

MATLAB/SIMULINK for training of neural networks.

The control signal for converters according to plant output

is generated by trained ANN on the basis of plant

identification. In this study use the different type of cases

are as follows:

a. Using only current controller b. Using only speed controller c. Single ANN controller with both current and

speed control

Fig.8 (a): Output motor current response

Fig.8 (b): Output motor speed response

a. Response of system using only current control strategy

with ANN: In this case reference plant have only current controller,

shown in Fig.10.The input and output data are generated

by this reference plant which is shown in Fig.12.The

complete plant layout is given in Fig.9.The neural network

specification are shown in Fig.11.The response of the

system with simulink plant model with ANN, using

current control strategy is shown in Fig.13.The result

shows that the response of the system is better than using

conventional PI controller.

simulink plant model using only current control strategy with ANN

0.7s+1

den(s)

motor

14.5

0.7s+1

load

1

.00138s+1

converter

Step1

ScopePlant

Output

Reference

Control

Signalf g

NARMA-L2 Controller

-K-

Gain

Fig.9: Simulink plant model using only current control strategy

with ANN


50

1

Out1

-K-

motor Gain

0.7s+1

den(s)

motor

14.5

0.7s+1

load

.4

current transducer

-K-

current controller Gain

0.0208s+1

s

current controller

.54

current amplifire

30

converter Gain

1

.00138s+1

converter

4.5

Gain

1

In1

Fig.10: Simulink reference plant model for training of ANN with

current controller

b. Response of the system using only speed control

strategy with ANN:

In this case plant layout is shown in Fig.14. Only change

the plant specification of ANN and reference plant model

which is shown in Fig.15&16. The input and output data

are generated by this reference plant which is shown in

Fig.17.The response of the system with simulink plant

model with ANN, using speed control strategy is shown in

Fig.18.The results show that the response of the system is

not so poor but the settling time is more in comparison to

(a).

Fig.11: ANN and Plant specification model with only current

control strategy

Fig.12: Plant input and output generated by reference plant for

ANN

c. Response of system using speed and current control with

ANN:

In this case only single neural network is used for both

speed and current control strategy which is shown in

Fig.19. Reference model for training of ANN with current

and speed controller is shown in Fig.20. The plant

specification and plant input output model with both

current and speed control strategy is shown in Fig.21 and

22. The response of the system is shown in Fig.23. The result of this system shows that the response of the plant is

so better in comparison to previous cases as well as

conventional PI control methods.

0 1 2 3 4 5 6 7 8 90

0.2

0.4

0.6

0.8

1

time(s)

speed(p

u)

final result

Fig.13: Plant output with current control strategy using ANN as

current controller

simulink plant model using only speed control strategy with ANN

-K-

motor Gain

0.7s+1

den(s)

motor

14.5

0.7s+1

load

1

.00138s+1

converter

Step1

ScopePlant

Output

Reference

Control

Signalf g

NARMA-L2 Controller

30

Gain

Fig.14: Simulink plant model using only speed control strategy

with ANN

Fig.15: Simulink reference model for training of ANN with

speed controller

Fig.16: ANN and plant specification model with only speed

control strategy


51

Fig.17: Plant input and output generated by reference plant for

ANN

0 1 2 3 4 5 6 7 8 90

0.2

0.4

0.6

0.8

1

time(s)

speed(p

u)

final result

data1

Fig.18: Plant output speed control strategy using ANN as speed

controller

final simulation plant

-K-

motor Gain k

0.7s+1

den(s)

motor

14.5

0.7s+1

load

1

.00138s+1

converter

Step

ScopePlant

Output

Reference

Control

Signalf g

NARMA-L2 Controller

30

Gain

Fig.19: Simulink plant model with current and speed control

using ANN

simulink reference plant model with current and speed control strategy

1

Out1

1

0.002s+1

techo genrator

-K-

speed controller Gain

0.0188s+1

s

speed controller

-K-

motor Gain

0.7s+1

den(s)

motor

14.5

0.7s+1

load

.98

feedback Gain

.4

current transducer

4.5

current controller Gain1

-K-

current controller Gain

0.0208s+1

s

current controller

.54

current amplifire

30

converter Gain

1

.00138s+1

converter

1

In1

Fig.20: Simulink reference model for training of ANN with

current and speed controller both

Fig.21: ANN and plant specification model with current and

speed control strategy

Fig.22: Plant input, output and ANN training error

0 1 2 3 4 5 6 7 8 90

0.2

0.4

0.6

0.8

1

time(s)

speed(p

u)

Fig.23: Plant output with current and speed control strategy using

single ANN

VI. RESULTS AND DISCUSSION

In this work actually evaluated the performance of a dc

motor with a constant load using different type of control

strategy conventional (PI) and modern (ANN) controller

concept. Using the ANN controller concept with dc motor

the performance and dynamics of the dc motor is

improved in comparison to the conventional PI controllers.

The simulation of the complete drive system is carried out

based on training for different reference plant with

different control strategy. The D.C. motor has been

successfully controlled using an ANN. Firstly, one ANN


52

controller is used with only Current control strategy. The

results with both speed and current control strategy are

better as compared to the results obtained with only

current control and speed control strategy. The simulation

result (Fig.23) shows that the response of the plant with

both current and speed controller is better as compared to

conventional methods (Table 1). The results prove that the

complete D.C. drive system is robust to parameter

variations. All the comparisons for the different cases are

tabulated in Table 1.

Table 1: speed response

VII. CONCLUSION

By using ANN mode controller for the separately excited

DC motor speed control, the following advantages have

been realized.

The speed response for constant load torque shows the

ability of the drive to instantaneously reject the

perturbation. The design of controller is highly simplified

by using a cascade structure for independent control of

flux and torque. By using ANN don’t have to calculate the

parameters of the motor when designing the system

control. By using ANN the complete D.C. drive system is

robust to parameters variations. The dynamic and steady

state performance of the ANN based control drive is much

better than the PI controlled drives. Settling time has been

reduced to a label of 0.0.74 sec.

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[6] J.Santana, J.L. Naredo, F. Sandoval, I. Grout, and O.J.

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a DC series motor,” Mechatronics, vol. 12, issues 9-10, pp.

1145-1156, Nov.-Dec.2002.

[7] P.C. Sen, Principle of Electric Machines and Power

Electronics, John Wiley and Sons, 1989.

[8] J.H. Mines, MATLAB Supplement to Fuzzy and Neural

Approaches in engineering, John Wiley, NY,1997.

[9] S.G. German-Gankin, The computing modeling for power

electronics system in MATLAB, 2001.

[10] S. Hykin, Neural Networks, Macmillan, NY, 1994.

[11] E. Levin, R. Gewirtzman, and G.F. Inbar, “Neural Network

Architecture for Adaptive System Modeling and Control”,

Neural Networks, no. 4 (2), pp 185-191,1991..

[12] Demetri Psaltis, Athanasios Sideries and Alan A.

Yamamura,” A Multilayered Neural Network controller,”

IEEE International conference 1981.

[13] D.E.Rumelhart, G.E. Hinton and R.J. Williams, Parallel

Distributed Processing, Chapter 8: Learning internal

representations by error propagation,” vol.1, MA, MIT

Press, 1986.

[14] G.M. Scott, “Knowledge- Based Artificial Neural Networks

for Process Modelling and Control”, PhD. Thesis,

University of Wisconsin, 1993.

[15] A. K. Singh, A.K. Pandey, “Intelligent PI Controller for

Speed Control of SEDM using MATLAB” International

Journal of Engineering Science and Innovative

Technology(IJESIT), vol 2, no.1, Jan. 2013.

[16] G. M. Rao and .B.V. Sanker Ram, “A neural network based

speed control for DC motor”, International Journal of

Recent Trends in Engineering, vol. 2, no.6, November 2009.

[17] Zilkova, J., Timko, J., & Girovsky, P, “Nonlinear System

Control Using Neural Networks,” Acta Polytechnica

Hungarica, vol. 3, no. 4, pp. 85-89, 2006.

APPENDIX

The following motor parameters and ratings are used for

designing speed-controlled dc motor drives, maintaining

the field flux constant.

Power rating = 5HP,

D.C. motor input voltage = 220V,

Armature current rating = 8.2A,

Rated speed = 1470 rpm,

Armature resistance Ra = 4 Ω,

Moment of inertia J = 0.0609 kg-m2,

Armature Inductance La = 0.074H,

Viscous friction coefficient Bt = 0.0867 Nms/rad,

Torque constant Kb = 1.23 V/rad/s.

Converter Supplied voltage = 230 V,

3 – Phase, A.C. Frequency = 50 Hz,

Maximum control input voltage is ± 10 V.

Maximum current permitted in the motor is 20 A.

Number of training sample is 500.

Number of training epoche is 150

Number of hidden layers is 2.

BIOGRAPHIES

Amit Kumar Singh received his M.tech

degree in Power Electronics and Drives from

M.M.M. Engineering College, Gorakhpur,

(U.P) in 2012. He did his B.Tech in

Electrical Engineering from R.G.E.C Meerut

in 2009. Currently he is working as Assistant

Professor in Electrical and Electronics

Department in SCERT Barabanki, (U.P.).

His areas of current interest include electrical machines, control

Cases

Settling

time ts

(sec.)

Maximum

overshoot

(mp)

p.u.

Steady

state

error

(p.u.)

(A)

Conventional

control (PI)

For

speed 1.8 1.7 0.02

For

current 1.7 1.0 0.03

(B)

Modern

control (ANN)

I 0.85 No

overshoot 0.03

II 0.95 No

overshoot 0.04

III 0.74 No

overshoot 0.02


53

systems, power electronics and electric drives.

Ashok Kumar Pandey received his Ph.D.

degree in Electrical Engineering from Indian

Institute of Technology, Roorkee in 2003. He

did his M.Tech. in Power Electronics,

Electrical Machines and Drives from Indian

Institute of Technology, Delhi in 1995.

Currently, he is working as an Associate

Professor with the Department of Electrical

Engineering at M.M.M. Engineering College, Gorakhpur, (U.P.),

India. His areas of interest include power electronics, electrical

machines, and drive.

Manjari Mehrotra received his M.Tech

degree in Power Electronics and Drives from

M.M.M. Engineering College, Gorakhpur,

(U.P) in 2012. She obtained her B.Tech

degree in Electrical Engineering from

R.G.E.C Meerut in 2009. Currently she is

working as Assistant Professor in Electrical

and Electronics Department in SCERT

Barabanki, (U.P.). Her areas of current interest include electrical

machines, power electronics and electric drives.

Mar 2013

Xiaozhong Liao


54

Control Strategy with Game Theoretic Approach in DC

Micro-grid

Mingxuan Wu 1

Lei Dong 2

Furong Xiao 3 4

Abstract–This paper proposes a decentralized control

algorithm for DC micro-grid which is based on the game

theory without communication, the proposed algorithm is an

application of the Nash certainty equivalence principle. Since

it is achieved without communication, it benefits from

concerned reliability issues. Compared with the droop

control system, extensive analysis based on simulations

demonstrates that the proposed modeling, although

simplified, is sufficient for an adequate control system design.

The proposed control algorithm brings more accurate DC

bus voltage and good current sharing performance. The

simulation results verify the voltage stability and accuracy of

DC bus, and current-sharing control of DC-DC converters

are achieved simultaneously.

Keywords–Nash certainty equivalence principle, DC Micro-

grid, game theory, distribute generation

I. INTRODUCTION

Nowadays, energy and environmental problems are

interrelated with the factors, such as the growth of energy

demand, and the high quality with safe and reliable

electric requirement. Against the background of these

problems, a large number of distributed generations (DGs)

are being installed into power systems. However, it is well

known that an insertion of many DGs affects power

quality of the utility grids, and it may cause problems such

as rising of voltage and protection problem. In order to

solve these problems, one of the solutions is to construct a

new power system, i.e. micro-grids which have been

especially researched all over the world [1]. DC

distribution micro-grids are suitable for those kinds of

energy storages and DGs, which can reduce conversion

losses and supply high quality power [2]. There are some

advantages using DC micro-grid in practice [3].

In the literature, most control strategies depend on a

communication infrastructure. Reference [4] presents the

operation of a multi-agent system for the control of a

micro-grid. The expensive communication system can be

avoided by using active power/frequency droop control in

the conventional grid control system [6,7]. An improved

droop control principle is presented for the control of

generators in an islanded micro-grid [8]. The droop control

method is a good solution for load sharing. However, the

conventional droop method also has several drawbacks

including a slow transient response, a trade-off between

load sharing accuracy and voltage deviation [12]. The load

sharing accuracy is affected by line, DG output

impedances and corresponding voltage drops. To improve

The paper first received 18 Dec 2012 and in revised form 13 .

Digital Ref: APEJ-2013-04-416 1,2,3,4

School of Automation, Beijing Institute of Technology, Beijing, 1 E-mail: [email protected],

corresponding author

2 E-mail: [email protected]



the accuracy of load sharing, increased droop gain scheme

is adopted. However, increased droop gain has a negative

impact on the overall system stability. Moreover, it

increases the range of system voltage variations [13-15].

In this paper, a control strategy is proposed based on the

game theory which does not depend on communication

infrastructure. As is shown in the Fig. 1, the multiple DG

system is modeled and employs game theory [9] to design

control strategy. The control strategy can minimize output

voltage error. It is found that performance of each DG is

practically independent in the system.

DG1Game

Controller1

DG2Game

Controller2

DGnGame

Controllern

...

DC Line Bus

EnergyStorage

Distribute Load

Fig.1: Multi-circuit system without communication

II. DECENTRALIZED CHARGING CONTROL PROBLEMS

FOR PCS IN MICRO-GRID

The decentralized DGs charging control problem is a form

of non-cooperative game, where a large number of selfish

DGs transfer the electricity resources to the DC line bus to

ensure the DC bus voltage stable. This paper presents a

novel control strategy that achieves Nash equilibrium by

simultaneously updating each DG’s best individual

strategy with respect to minimize the cost function. The

algorithm is unrelated to the number of DGs, since they

update their control strategy simultaneously and

independently. The proposed decentralized charging

control strategy drives the system asymptotically to a

unique Nash equilibrium.

The proposed algorithm is an application of the so-called

Nash certainty equivalence principle. The control

algorithm can achieve optimality of the micro-grid, i.e. it

can make the DC bus voltage stable and load sharing.

Nash equilibrium is the most important concept in game

theory. In fact, Nash equilibrium is a kind of “stalemate”

in which no one is interested in changing [16].

Definition 1: A collection of control strategies

;nd n N is Nash equilibrium if each individual DG can benefit nothing by changing its own strategy

( ; ) ( ; )n n nn n n

J d d J d d

(1)

for all (0,1)nd , and all n N .

mailto:[email protected]:[email protected]:[email protected]

Mingxuan Wu et. al: Control Strategy with Game Theoretic…

55

where *

nd is the collection of control strategies of the

whole DGs without DG n [19].

In other words, *nd is the solution of minimum cost

function

* * * * * *

1 1 1arg min ( , , , , , , ),

1,2, , .

n n n n n Nd J d d d d d

n N

(2)

Therefore, *nd is the control strategy which can obtain the

minimum value of cost function ( )n nJ d .

If the two above-mentioned conditions are achieved by

each DG, the micro-grid will achieve the state of Nash

equilibrium, i.e. the DC micro-grid will keep voltage

stable and load sharing.

A. Virtual Rivals Strategy

Assuming there are 1n DGs supply power for the micro-grid which means there are n rivals for every DG. Estimation of supply power strategy for every rival will be

difficult to calculate because the workload is extremely

large. In this paper, a conception of virtual rivals is

introduced which means to take the other DGs as an

equivalent virtual rival. This will simplify the estimation

for every rival and it has advantages as follows: 1)

Simplicity: Reducing the number of rivals from n to 1 simplifies the model and the complexity of calculation

greatly, and 2) High estimating accuracy: Estimating

supply power strategy for n rivals, since the uncertainty is too much for every rival, so the estimating error is

relatively large [5]. When estimating the equivalent rival,

the randomness will be offset and the estimating accuracy

is enhanced.

By this way, the method simplifies the n-player-game

problem to two-player-game problem that simplifies the

complexity of problem greatly. Therefore, in the

discussion of this paper, we only discuss the two-player-

game problem because it has the same result of n-player-

game problem.

B. Proposed Optimal Controller

The underlying decentralized DGs charging control is a

non-cooperative dynamic game. Each DG shares other

DGs with the information by DC line bus voltage. So we

need formulate the decentralized DGs charging control

problem as a dynamic games.

We consider charging control of each DG of size M with

the charging time {0,1, , 1, , 1, , }t T T T

where T denotes the ultimate charging steadily instant. The serial number of DG is denoted as

{0,1, , , , }M n N . With a control strategy of micro-

grid with game theoretic approach, we assume that DGs

achieve Nash equivalence at time T . The objective is to

implement a collection of DGs charging strategy that

achieves dual objectives, 1) the DC line bus voltage

achieves setting value of voltage, and 2) each DG achieve

the state of current sharing.

The objective of the control is to minimize the output

voltage error. Hence, a definition of the cost function of

each DG n is given by 1

2 2

1 2 3

0

12 2

1 2 3

0

( , ) ( ) ( )

( ) ( )

m t

n r m m r t

m

m t

t t r m m r t

m

J u i AP B k u k u k i D u u

Au i B k u k u k i D u u

(3)

where， A , B , D ,1

k , 2

k and 3

k are all non-negative

constant, P represents the output power of the each DG, u and i denote the output voltage and current of the each

PC, ru is the voltage reference of the DC line bus.

As is shown in (3), the output current, voltage and error of

the system voltage output are included in the cost function.

Where AP denotes the output power, which has the minimization of the input to the system results in

minimum input energy (minimum cost). Where 1

2

1 2 3

0

( )m t

r m m

m

B k u k u k i

determines the penalty for

deviating from the setting value, and 2

( )r t

D u u denotes

minimization of the output error that is one of the main

targets of the system. It will be shown that the presence of

the squared deviation term ensures convergence to a

unique collection of locally optimal strategies which is

Nash equilibrium [11]. The cost incurred in deviating from

the voltage reference of the DC line bus.

This paper proposes a control scenario which individual

DG minimize its own operating cost function (3). In order

to minimize its own operating cost, it is adopted by

calculate method of the extreme value of binary function

[10].

Therefore, we can demonstrate using the control law (4)

and (5) can minimize its cost function (3). The control law

can be simplified as: 1

2

1 2 3

0

2( ) 2 ( )

m t

r r m m r t

m

Bki k u k u k i D u u

A

(4)

and

1 2 3 .r

ik k k

u (5)

According to the transformation in (4) and (5), through the

voltage reference ru ,the previous voltage mu and current

mi ( 0,1, , 1)m t and present voltage tu can calculate

the reference current ri which can be obtained, and then

detect the output current i . Finally, PI adjust is adopted for a current closed loop to ensure a suitable power output.

The local information such as output voltage u and output current i can be detected directly. It is obviously that only local information can minimize the cost function.

Accordingly, using this method can achieve desired

performance in voltage regulation and current sharing


56

among the DGs. Such a structure has notable advantages

such as simplicity and reliability. And this method can

satisfy the most important characteristics of the micro-grid,

i.e. plug and play. DG can be considered as different

agents. Assuming each agent is ‘rational’ which means

every agent always following the maximum of its own

benefit function. Finally, the micro-grid system achieves

the state of Nash equilibrium.

III. SMALL-SIGNAL MODEL OF GAME THEORETIC

STRATEGY

A linear model is necessary for designing linear controls.

An average model is sufficient for the bandwidth

requirements of typical applications [17]. Accordingly, a

simple average model for the buck converter is developed

based on ideal transform concepts for switching. The DG’s

converter shown in Fig. 3 can be replaced by an average

model.

+

-

L

RC

1V+

-

1x

2x y

c

p

a

Q

Fig. 3: The module of buck converter

At time [0, ]t d T , the switch Q is turned on,

( ) ( )

( ) ( )

a c

cp ap

i t i t

u t u t

(6)

where d is the duty cycle of the switch Q , ai is the input

current of terminal a , ci is the output current of terminal

c . cpu and apu is the voltage between terminals a , p

and c respectively.

At time [ ,1]t d T , the switch Q is turned off,

( ) 0

( ) 0.

a

cp

i t

u t

(7)

Ideal transformer averaging concepts can be directly

applied to buck converter. A large signal average model

can be formed with transformers by realizing (6) and (7)

and similar average current equations,

( ) ( )

( ) ( ) .

a c

cp ap

i t i t d

u t u t d

(8)

The small signal model is formed from the large signal

model by perturbing the large signal parameters about a

particular operating point:

ˆ ˆ ˆ, ( ) , ( ) ,cp cp cp ap ap ap

d D d u t V u u t V u

ˆ ˆ( ) , ( ) ,a a a c c ci t I i i t I i

where the set { , , , , }ap cp a c

D V V I I defines a particular

operating point, and the set ˆ ˆ ˆˆ ˆ{ , , , , }ap cp a c

d u u i i defines

perturbing. The nonlinear model for the converter

operating in the continuous conduction mode is given by

ˆˆ ˆ

ˆˆ ˆ .

a a c c

cp cp ap ap

I i I i D d

V u V u D d

(9)

The dynamic model given in (9) is nonlinear and cannot

be directly employed to design a control system with the

most commonly used techniques, which require a linear

model. However, if the magnitudes of the perturbations

are much smaller than their steady-state values, the

nonlinear terms can be ignored without resulting in

significant error, and a linear approximation of the system

is obtained. Assuming dynamic components are much

smaller than steady-state components,

ˆ ˆ ˆˆ ˆ1, 1, 1, 1, 1.

ap cp a c

ap cp a c

u u i id

D V V I I (10)

So the infinitesimal of higher order ˆˆc

i d and ˆˆap

u d

can be neglected. Hence, (10) can be divided into steady-

state component and perturbing component respectively.

Steady-state components

.

a c

cp ap

I I D

V V D

(11)

Perturbing component

ˆˆ

ˆˆ ˆ .

a c c

cp ap ap

i i D I d

u u D V d

(12)

Thus, a small-signal reduced-order linear model for the

buck converter can be defined as Fig. 4.

+

-

L

RC

1V+

-

-

+ 1: Dˆˆ

L Li D I d

1 ˆV dD

ˆLI d 1 1

ˆV̂ D V d

ˆLi

ˆoV

+

-

Fig. 4: The small-signal equivalent circuit model of buck

converter

Table 1: Parameters of the small-signal equivalent circuit

model.

Parameters Values Unit

Output inductor 10e-2 H

Resistance of load 20 Output storage capacitor 300e-6 F

Load 20 Switching frequency of

the converter

2 kHz


57

The parameters of the small-signal model are given in

Table 1, the transfer functions (13) and (14) can be easily

obtained applying the Laplace transform in (12) assuming

zero initial conditions

2

1/ /

ˆ ( )( )

ˆ 1 / 1( ) / /

o invd

Rv s UcsG s

s LC sL Rd s R Lscs

(13)

0

2

0

ˆ ˆˆ ( )( ) ( )( )

ˆ ˆ ˆ( ) ( ) ( )

11( ) .

1 / 1/ /

ˆ ( )( )

ˆ( )

oL L

id

o

in

vd

L

vd

v si s i sG s

d s d s v s

sCR UG s

s LC sL R RR

Cs

i sG s

u s

(14)

Therefore, the open loop small-signal model without game

theoretic control is obtained, and the bode plot of ( )vd

G s

is shown as Fig. 5,

-20

-10

0

10

20

30

40

Magn

itud

e (d

B)

101 102 103-180

-135

-90

-45

0

Phas

e (d

eg)

Bode Plot

Frequency (HZ)

Fig. 5: The bode plot of ( )vd

G s

As is shown in the Fig.5, phase margin is only about 10,

the system is in a critical steady state. When the proposed

game theoretic control is adopted, the close loop structure

is illustrated in Fig.6.

+-

+

-

e d1G (s) 2G (s)

idG (s)

vdG (s)ˆ

ou (s)ˆ

o_refu (s)ô_refi

1K

2K

3K

++

’K+ -

+

+ ôi

Fig. 6: The closed loop structure of circuit with game theoretic

control

The equations of control are

'

_ 1 _ 2 3 _

1ˆ ˆˆ ˆ ˆ ˆ( )+ ( )o ref o ref o o o ref o

i K k v k v k i K v vs

(15)

_

1ˆ ˆ ˆ( )( ).o ref o P I

d i i K Ks

(16)

Combine the (15) with (16)

'

1 _ 2 3 _

' '

1 _ 2 3

' '

1 _ 1 1 2

1 1ˆ ˆ ˆˆ ˆ ˆ ˆ( )+K ( ) ] ( )

1 1 1 1ˆˆ ˆ[( ) ( ) ( 1) ] ( )

ˆˆ ˆ[( ( ) ) ( ( ) ) ( ( ) 1) ] ( )

o ref o o o ref o o P I

o ref o o P I

o ref o o

d K K v K v K i v v i K Ks s

KK K v KK K v KK i K Ks s s s

KG s K v KG s K v KG s i G s

(17)

where 1

1( )G s K

s ，

2

1( )

P IG s K K

s ， 2

2BKK

A

.

Assuming the input voltage 20in

U V , the parameters are

given as fallows, 0.01K ,'

0.5K , 0.5P

K , 1I

K ,

11K ,

20.8K ,

30.2K . The open loop gain of

current can be given by

2 2 2

_ 2 5 3 2 2

6 10 10.12 20( ) .

6 10 10 20k i id

s sT s G G

s s s

(18)

Also, the bode plot can be obtained as Fig. 7.

-40

-20

0

20

40

Magn

itud

e (d

B)

10-2 10-1 100 101 102 103 104-90

-45

0

45

Phas

e (d

eg)

Bode Plot

Frequency (HZ)

Fig. 7: The bode plot of current loop

As is shown in the Fig. 7, phase margin is about 110, the

design of current loop is in a steady state. Therefore, the

close loop structure with game theoretic control in Fig. 6

can be simplified as Fig. 8.

+

-

e d2vd2

G

1+G G (s)

ôu (s)

' id2 3

' vd1

G1 S(K +K +K )

KS GK +K

K

'1

SK +K

K

1K

S vdG (s)

ô_refiô_refu (s)

Fig. 8: The simplify close loop structure of circuit with game

theoretic control

As is shown in the Fig. 8, the overall open-loop transfer

function is obtained by

'

1

'

2 3

2

2

4 4 2 3 2

11 6 8 5 5 4 2 3 2

'

2 3

'

1

2

2

1

1 1( ) ( )

1 ( )

3 10 5.06 10 100 208 0.2.

18 10 24 10 18.536 10 8.5 10 30.12 20

1( ) ( )( )

1vd vd vd id

vd

id

vd

v

vd

SK K K

K S

G s K G K K G KK G

S S

G

G G s

s s s s

s s s s s s

GSK K K

S K GK K

K

T s

G

G G

(19)

Through the overall open-loop transfer function, the bode

plot can be obtained as Fig. 9.


58

-100

-50

0

50

100

Magn

itud

e (d

B)

10-6 10

-4 10-2 10

0 102 104-180

-135

-90

-45

0

Phas

e (d

eg)

Bode Plot

Frequency (HZ)

Fig. 9: The bode plot of overall open loop transfer function

From Fig. 9, it can be seen that phase margin is about 80,

the system is in a steady state.

Through the small-signal model of the system control with

game theoretic strategy, the design of the controller is

stable.

IV. NUMERICAL SIMULATION

In this part, by using the concept of virtual rival strategy, a

system composed of two DGs with a resistive load and a

storage device is used for simulate the micro-grid system.

In this paper, we adopt the buck converter as the main

circuit of controller. One DG is consisted of photovoltaic

generator and its controller, and the other DG is consisted

of wind turbine and its controller. The simulation structure

of simplified system of micro-grid is shown as Fig.10, and

the parameters of the model are as follows: the output

inductor is 10e-2 H, the resistance of load is 20 , the

switching frequency adopt 2 kHz.

R Cou

DC BUS

controller

controller

PV

WIND

1i

2i

Fig. 10: Simulation structure of simplified system of micro-grid

A. Simulation Experiment

According to the design parameters above and the

reference value of the DC line bus voltage is 20V. The

results obtained from simulations in MATLAB are

represented in Fig. 11, Fig. 12 and Fig. 13which show the

state of micro-grid with different control methods. The

current of each DG is shown in the upper picture, and

voltage of DC line bus is shown in the lower picture. At

the upper picture, the two curves indicate the current of

photovoltaic generator and wind generator circuit

respectively.

When two DGs are adopted open loop control, the results

of current share mainly depend on the symmetry of

module parameters. As is shown in the Fig. 11, it is clear

that the voltage is maintained in 20V and the performance

of the current sharing is bad. Although using the open loop

control can meet the voltage regulation, the performance

of the current sharing is not ideal.

When the micro-grid system adopt the droop control

strategy, as is shown in Fig. 12, it is clear that the output

current of each circuit is almost the same, and the error of

current is less than 5%. However, the voltage of DC bus is

only maintained about 17V which causes a drop in voltage

regulation. Although using the traditional droop strategy

can meet the request of output current sharing, the

regulation of DC line bus voltage is not ideal.

Compared with the traditional droop control strategy and

directly parallel strategy, the game controller has a good

performance on voltage regulation and current sharing. As

is shown in the Fig. 13, it is clear that the output current of

each circuit is almost the same and the voltage is

maintained in 20V. In addition, the regulation time of

game system is as long as the traditional controllers which

adopt the droop strategy. In conclusion, the game theoretic

method is possible to control each system rapidly and

independently.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.050

1

2

3

4

5

6

7

The

outp

ut c

urre

nt o

f Eac

h PC

(A)

T(s)

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.050

5

10

15

20

25

Dc li

ne b

us v

olta

ge U

(V)

T(s)

Fig.11: State of micro-grid system with the open loop control

strategy

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.050

1

2

3

4

5

6

7

T(s)

Th

e o

utp

ut

curr

ent

of

Eac

h P

C(A

)

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.050

2

4

6

8

10

12

14

16

18

20

Dc

line

bu

s vo

ltag

e U

(V)

T(s)

Fig.12: State of micro-grid system by droop control method

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.050

1

2

3

4

5

6

The

outp

ut c

urre

nt o

f Eac

h P

C(A

)

T(s)

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.050

5

10

15

20

25

T(s)

Dc

line

bus

volta

ge U

(V)

Fig.13: State of micro-grid system by game theoretic strategy

method


59

B. Dynamic Response

In order to study the controller performance to large

transients, a variable load is implemented (a load of 10

is turned on in the micro-grid output). In this part, the

reference value of the DC line bus voltage is 24V. The Fig.

14, Fig. 15 and Fig. 16 show the load change in the micro-

grid when time arrive at 0.05s.

Fig. 14, Fig. 15 and Fig. 16 present the experiments for a

load step from 100% to 50% of the output power. During

this transient, an overshoot of less than 5% is observed in

the output voltage with a good regulation as required. At

the same time, the current of each DG changes

synchronously, which achieves current sharing state

finally.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

5

10

15

20

25

30

35

T(s)

Dc

line

bus

volta

ge U

(V)

Fig.14: Voltage of dc line bus when load change in 0.05s

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.5

1

1.5

2

2.5

T(s)

The

outp

ut c

urre

nt o

f DC

line

bus(

A)

Fig.15: Current of dc line bus when load change in 0.05s

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

The

outp

ut c

urre

nt o

f Eac

h PC

(A)

T(s)

Fig.16: Current of each PC when load change in 0.05s

C. Experimental Result

An experimental result is produced by laboratory

prototype, as shown in Fig. 17. This prototype consists of

two PV simulators, and their buck converters connected to

a stand-alone DC system which has an output storage

ultra-capacitor and an adjustable resistive load. The

simplified system is shown in Fig. 10.

The Fig. 17 and Fig. 18 show the measured waveform for

a step load increase. 100% load is increased at t = 370s,

causing a transient step up of the output current

waveforms of two DGs. The experimental results of the

microgrid voltage are depicted in Fig. 17, which shows the

change of the DC bus voltage due to the variations of the

load. Fig. 18 shows the output current of each DG

converter. During the dynamic process, the current sharing

is achieved by the two DGs. The measured current

waveforms in Fig. 17 show the rapid response of the

current-regulated. At the same time, the voltage of DC bus

keeps the reference value stable in 24V.

0 100 200 300 400 500

12

16

18

20

22

24

26

30

28

10

8

6

4

2

0

T(s)

me

as

ure

d v

olt

ag

e (V

)

DC bus voltage measured by converter I

DC bus voltage measured by converter II

Fig. 17: Measured voltage of each converter when load steps

increase at 370s

0 100 200 300 400 500

2

2.5

3

3.5

4

4.5

T(s)

ou

tpu

t cu

rre

nt（

A）

Output current of converter I

Output current of converter II

Fig. 18: Measured output current of each converter when load

steps increase at 370s

V. CONCLUSION

In this paper, the game controller is applied to DGs and it

can be seen that using this method achieves desired

performance in voltage regulation and current sharing

among the micro-grid system. In order to simplify the

analysis, we adopt the concept of virtual rival strategy that

simplifies the n-player-game problem to two-player-game

problems.

A small-signal stability analysis of the proposed control

approach was shown. In addition, the proposed approach

has been tested extensively in simulation. The controller

allows DGs to share power generation without

communications, and the performance of dynamic

response is obtained by experimental results. It is

concluded that the new control strategy shows good results

in transient issues, power sharing, and stability.

REFERENCES

[1] H. Kakigano, Y. Miura, and T. Ise, “Low-voltage bipolar-type DC microgrid for super high quality distribution”,

IEEE Trans. Power Electron., vol. 25, no. 12, 2010.

[2] P.N. Enjeti, P.D. Ziogas and J.F. Lindsay, “Programmed PWM Technique to Eliminate Harmonics: A Critical

Evaluation”, IEEE Trans. Ind. Appl., vol. 26, no. 2, pp. 302-

315, March/April 1990.

[3] Y. Xiao, B. Wu, S. Rizzo and R. Sotuden, “A Novel Power Factor Control Scheme for High Power GTO Current

Source Converter”, Conference Record IEEE-IAS, pp. 865-

869, 1996.

[4] A. L. Dimeas and N. D. Hatziargyriou, “Operation of a multiagent system for microgrid control”, IEEE Transs on

Power Systems, vol. 20, no. 3, AUG. 2005.


60

[5] K. Border, Fixed Point Theorems with Applications to Economics and Game Theory. Cambridge, U.K.:

Cambridge University Press, 1985.

[6] S. Barsali, M. Ceraolo, P. Pelacchi, and D. Poli, “Control techniques of dispersed generators to improve the continuity

of electricity supply”, Power Engineering Society Winter

Meeting, vol.2, 2002, pp.789 794.

[7] K. D. Brabandere, B. Bolsens, J. Van den Keybus, A. Woyte, J. Driesen, R. Belmans, K.U. Leuven, “A voltage

and frequency droop control method for parallel inverters”,

Power Electronics Specialists Conference, vol.4, pp. 2501 -

2507.

[8] T. L. Vandoorrn, B. Meersman, L. Degroote, B. Renders, and L. Vandevelde, “A control strategy for islanded

microgrids with DC-link voltage control”, IEEE Trans. on

Power Delivery, vol. 26, no. 2, 2011.

[9] D. Fudenberg and J. Tirole, Game theory. MIT Press, 1991. [10] Mingming Chen, Advanced Mathematics, Beijing:

Chemical Industry Press, 2010- 2011.

[11] D. Smart, Fixed Point Theorems. London, U.K.: Cambridge University Press, 1974.

[12] J. Kim, Guerrero, J.M. Rodriguez, P. Teodorescu, R.K. Nam, “Mode adaptive droop control with virtual output

impedances for an inverter-based flexible AC microgrid”,

IEEE Trans. Power Electron., pp. 689 701, 2011.

[13] A. Haddadi, A. Shojaei and B. Boulet, “Enabling high droop gain for improvement of reactive power sharing

accuracy in an electronically-interfaced autonomous

microgrid”, Energy Conversion Congress and Exposition

(ECCE), pp. 673 679, 2011.

[14] L.B. Perera, G. Ledwich, A. Ghosh, “Distribution feeder voltage support and power factor control by distributed

multiple inverters”, Electrical Power and Energy

Conference (EPEC), pp. 116 121, 2011.

[15] Avelar, H.J, Parreira, W.A, Vieira, J.B, de Freitas, L.C.G, Coelho, E.A.A, “A State Equation Model of a Single-Phase

Grid-Connected Inverter Using a Droop Control Scheme

With Extra Phase Shift Control Action”, IEEE Trans. on Ind.

Electronics, pp. 1527 1537, 2012.

[16] A. Y. Wang, J. Huang, C. Wu and H. Mohsenian-Rad, “Demand side management for wind power integration in

microgrid using dynamic potential game theory”,

GLOBECOM Workshops (GC Wkshps), pp. 1199 1204,

2011.

[17] B. Oraw, R. Ayyanar, “Small signal modeling and control design for new extended duty ratio, interleaved multiphase

synchronous buck converter”, Telecommunications Energy

Conference, 2006, pp. 1 8, 2006.

BIOGRAPHIES

Mingxuan Wu obtained his Bachelor degree

and master degree from Beijing Institute of

Technology. He is currently an engineer in the

Department of China Southern Power Grid. His

research interests are in the areas of DC microgrid system and new energy power

generation.

Lei Dong was born in 1967. He is currently a professor in Beijing Institute of Technology.His

research directions are power electronics and

power drive,and new energy power generation.

Furong Xiao obtained his bachelor degree from the Beijing Institute of Technology in 2011,and

still study for the PHD degree in this school.

His research direction is power energy conversion and micro grid.

Xiaozhong Liao was born in Guangdong, China,

in 1962. She received her BSc and PhD degrees

respectively from the Tianjin University in electrical and automation engineering and the

Beijing Institute of Technology in control

engineeering. She is currently a professer in Beijing Institute of Technology. Her research

intersts are the electric drive system and energy

converter control.

-

-

-

-

-

-

-

M. Rajesh et. al: Three Phase Double Boost PFC Rectifier…

61

Three Phase Double Boost PFC Rectifier Fed SRM Drive

M. Rajesh 1 B. Singh

2

Abstract: This paper deals with a three phase double boost

PFC(power factor correction) rectifier fed SRM (Switched

Reluctance Motor) drive. The proposed system consists of

two boost converters with DC outputs connected in series to

feed a midpoint converter fed SRM drive. This system needs

only two active switches at rectifier side and a midpoint

converter needs only one active switch per phase. Besides, it

provides balanced DC link capacitor voltages with improved

power quality at AC mains. The proposed three phase double

boost PFC rectifier fed SRM drive is designed, modeled and

its performance is simulated in MATLAB/Simulink. The

performance of proposed system is compared with a six pulse

diode bridge converter fed SRM drive.

Keywords–Midpoint converter, power quality, switched

reluctance motor, Boost PFC rectifier, Scott transformer.

I. INTRODUCTION

A switched reluctance motor (SRM) has the simplest

construction and is economical among other electrical

motors. It has several advantages as a variable speed drive

as it can operate in wide speed range. However SRM

cannot be operated directly from AC or DC supply, it

requires power converts for its operation. The most

commonly used converter is a midpoint converter since

only one switch per phase is needed thus reducing the cost

of drive [1]. All these converters need DC supply or AC

supply with a rectifier. Fig.1 shows six pulses diode bridge

rectifier fed midpoint converter based SRM drive. The

disadvantage of this configuration is that it generates

harmonics to the AC mains with low input power factor.

+-ω*

Speed

Controller

G

ω

Ik

d

dt

Reference

Current

Generator

Current

Controller

Ik* 4

Vdc

SRM

Vc1

Vc2C

C+

-

Phase

currents

Hall

sensor

A

B

C

D

N

Mid point Converter

G1G3

G2G4

Ө

415V,3Φ,50Hz

ias

ibs

ics

Ls

Ls

Ls

Fig.1: Six pulse diode bridge rectifier fed SRM drive

Three phase active PFC boost rectifiers are preferred in

industries due to their high efficiency, low EMI emission

and improved power quality at AC mains. Most commonly

used PFC boost rectifiers are multilevel boost rectifier,

Vienna rectifier and third harmonic modulated rectifiers.

Different configurations of multilevel rectifiers are given

The paper first received 23 Jan 2013 and in revised form 14 July 2013.

Digital Ref: APEJ-2013-05-419 1

Department of Electrical Engineering, Indian Institute of Technology

Delhi, E-mail: [email protected] 2

Department of Electrical Engineering, Indian Institute of Technology

Delhi E-mail: [email protected]

in [2-5]. Multilevel reduce the voltage stress across active

switches and operate at lower frequencies. However, these

rectifiers need more number of active switches and control

of capacitor voltages becomes difficult with increase in

levels. A simple three phase NPC three level rectifier

needs twelve active switches. The multilevel rectifiers are

capable of operating in all four quadrants [6]. Vienna

rectifier [7-12] is a boost rectifier which requires only

three active switches and its control is simple. This

rectifier has short circuit immunity to failure of control

circuit, immunity towards voltage unbalance and voltage

variations. Third harmonic modulated rectifier is explained

in [13-15]. It consists of third harmonic current injection

network to inject third harmonic current at AC side of

rectifier to improve power quality at AC mains.

Minnesota rectifier [16] is one of the most commonly used

rectifier which uses third harmonic current injection

technique. This rectifier needs only two active switches

and a zig zag transformer is used to inject third harmonic

current at AC side of rectifier. All these converter

topologies do not provide isolation. However in many

applications isolation is required between AC mains and

the drive.

Three phase double boost PFC rectifier fed midpoint

converter based SRM drive is recommended in this paper

for improving power quality at AC mains. In this system

the outputs of two single phase boost PFC rectifier are

connected in series to form split DC bus voltage. The input

of these boost rectifiers is connected to Scott connected

transformer which provides isolation. The voltage stress

on the active switches and the diodes of this boost rectifier

is equal to half of DC link voltage. The proposed SRM

drive is designed, modeled and its performance is

simulated using MATLAB/Simulink environment and the

performance is also compared with a conventional six

pulse diode bridge rectifier fed SRM drive. The power

quality of the proposed drive system is found within IEEE

519 standard limit [17].

II. SYSTEM CONFIGURATION

The schematic diagram of three phase double boost PFC

rectifier fed midpoint based SRM drive is shown in Fig.2a.

Two single phase AC supplies with 900 phase shift are

obtained from Scott connected transformer and given to

two single phase boost rectifier. The outputs of single

phase boost rectifiers are connected in series and form

split DC bus voltages which are connected to a midpoint

converter based SRM drive. The connection diagram and

phasor diagram of Scott connected transformer is shown in

Fig.2b. Two single phase transformers are used to obtain

three phase to two single phase conversion. One of the

transformers is called teaser transformer and has the turns

ratios of 0.866V:V1 and other transformer called main

transformer has midpoint at primary winding having turns

ratio of 0.5V - 0.5V:V2. Where V is the magnitude of


62

supply line voltage, V1 and V2 are secondary voltages of

PI Controller+-

Vc1

*

Vc1

ABSv11Vm

+-

iL1

Kc sa

PI Controller+-

Vc2

*

Vc2

ABS1Vm

+-

iL2

Kc sb

>=

Comp

>=

Comp

iL1*

iL2*

ut1

ut2

Im1

Im2

v2

Fig.2 (c): Control of three phase double boost PFC rectifier

the transformers. Two single phase boost rectifiers are

controlled independently by sensing their inductor currents.

A small rating capacitor Cf is connected at the secondary

terminals to eliminate higher order harmonics.

III. DESIGN OF THREE PHASE DOUBLE BOOST PFC

RECTIFIER

Three phase double boost PFC rectifier consists of a two

single phase transformers, two boost inductors, two DC

link capacitors, two active switches and ten diodes. The

design of proposed converter system is explained below.

A. Design of Boost Inductor For a 4kW, 8/6 pole SRM drive, an input power is

considered as 4.4kW including losses. The value of boost

inductor (L=L1=L2) is calculated as [18],

in

s

V DL

If

(1)

where Vin and D are defined as,

12 2

in

VV

(2)

1

1

-c in

c

V VD

V (3)

where Vin is the DC output voltage of bridge rectifier, V1

is the secondary terminal voltage of transformer, D is duty

ratio, ΔI is the inductor ripple current, Vc1 is the output

voltage of boost rectifier and fs is switching frequency.

The input power 4.4kW is shared by PFC boost rectifier

equally. Hence the supply current drawn by the boost

rectifier with transformer secondary voltages V1 = V2 =

180V is calculated as,

1

220012.22

180

boostP

I AV

(4)

Since same current flows through inductor the ripple

current (ΔI) in the inductor at 12% ripple is calculated as,

ΔI = 10% x I = 1.222A (5)

Taking duty switching frequency fs as 20 kHz, DC link

voltage Vdc as 560V and Vc1 as 280V (Vdc/2 = 560/2), from

eqns. (1-5), the obtained value of boost inductor is L is

2.8mH, hence L1 and L2 are selected as L1 = L2 = 3mH.

B. Design of Capacitor To assure DC link voltage within limit for three phase

double boost PFC rectifier the DC link capacitor (C1, C2)

is calculated as [18],

1 2 21

IdC CV

c

(6)

where ΔVc1 is the ripple voltage across capacitor, ω =2пf

is angular frequency of supply voltage and f is supply

frequency and Id is DC link current.

DC link current Id is calculated as,

in

d

dc

PI

V (7)

Taking Pin as 4.4kW, Vdc as 560V, f as 50Hz and ΔVc1 as

2% of Vc1, the obtained value of Id is 7.851A and obtained

value of C1 is 2233µF, hence C1 and C2 are selected as

2200µF.

C. Design of Transformer For converting three phase 415V AC mains to two single

phase voltages of each of 180V, the required turns ratio(n1,

n2) of single phase transformers needed for Scott’s

connection is calculated as,

Teaser transformer 1

1

0.866Vn

V (8)

AC Mains

L1

L2

sa

sb

Cf

Cf

+

-

Vdc

Vc1+-

C

C+

-Vc2

N

SRM

B

C

D

A

Mid point Converter

G1

G2

G3

G4

iL1

iL2

415V,3Φ,50Hz

ias

ibs

ics

Ls

Ls

Ls V1

V2

V

0.5V 0.5V

V

0.8

66

V

a1

a2

a3

m

v1

v2

v

v

a1

a2a3 m

v1

v2

main

Teaser

Fig.2 (a): Three phase double boost PFC rectifier fed SRM drive Fig.2 (b): Scott connected transformer and its phasor

diagram

M. Rajesh et. al: Three Phase Double Boost PFC Rectifier…

63

Main transformer 2

2

0.5 - 0.5V Vn

V (9)

where V is the AC mains voltage, V1 and V2 are secondary

voltage of transformers, with V = 415V and V1 = V2 as

180V, the calculated value of turns ratio are n1 = 359.5/180

and n2 = 207.5-207.5/180.

IV. CONTROL OF THREE PHASE DOUBLE BOOST PFC

RECTIFIER FED SRM DRIVE

The control algorithm of three phase double boost PFC

rectifier is shown in Fig.2c. The boost rectifiers are

controlled independently by sensing boost inductor current.

The gate signals are generated by carrier based PWM

controller. Each boost rectifier consists of capacitor

voltage controller, reference boost inductor current

estimator and boost inductor current controller.

A. Capacitor Voltage Controller The reference capacitors voltages (Vc1

* and Vc2

*) of two

boost PFC rectifier are compared with the sensed

capacitors voltages (Vc1 and Vc2). The resulting capacitors

voltage errors (Vc1e and Vc2e) at nth

instant are given as,

*

1 1 1( ) ( ) - ( )

c e c cV n V n V n (10)

*

2 2 2( ) ( ) - ( )

c e c cV n V n V n

(11)

The PI (Proportional Integral) voltage controllers are used

to get reference currents Im1* and Im2

* and are given at n

th

sampling instant as,

* *

1 1 1 1 1 1 1( ) ( -1) { ( ) - ( -1)} ( )

m m p c e c e i c eI n I n K V n V n K V n (12)

* *

2 2 1 2 2 1 2( ) ( -1) { ( ) - ( -1)} ( )

m m p c e c e i c eI n I n K V n V n K V n (13)

where the outputs of capacitor voltage controllers at nth

are

Im1*(n) and Im2

*(n) and for (n-1)

th instant are Im2

*(n-1)

and Im2*(n-1). These capacitors voltage error at n

th instant

is given by Vc1e(n) and V\c2e(n) and for (n-1)th

sampling

instant are Vc1e(n-1) and V\c2e(n-1); Kp1 and Ki1 are

proportional and integral gains of the DC capacitor

voltage controllers.

B. Reference Boost Inductor Current Estimation Unit templates of secondary side voltage of Scott’s

transformer are given as,

0

11

22

( ( ))( ) sin( ) ;

( ( ))( ) sin( -90 )

tm

tm

abs v tu t t

V

abs v tu t t

V

(14)

where Vm is the amplitude of transformer secondary

voltages.

The reference inductors currents (iL1* & iL2

*) are estimated

as,

* * * *1 1 1 2 2 2( ) ( )L m t L m ti I u t and i I u t (15)

C. Boost Inductor Current Controller Fig.2c shows the controller of the three phase double boost

PFC rectifier. The reference boost inductor currents are

compared with sensed currents and the current error is

processed through a proportional current controller of gain

Kc. This output of current controller is fed to the carrier

based PWM generator. The carrier based PWM generator

consists of a comparator and a triangular carrier wave of

20kHz. The output of current controller is compared with

carrier wave to generate PWM signal and given to

switches Sa and Sb..

V. CONTROL OF SRM

The rotor speed of SRM is compared with reference speed

and the speed error is processed through a speed

proportional integral (PI) controller. The error speed (Δωe)

at nth

instant is given as,

Δωe(n) = ωe*

(n) - ωe(n) (16)

The PI speed controller generates reference motor current

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